Hi,I'm trying to construct something giving me a ratio between realized and implied volatility on the swaption market.So : 1. i compute the forward rates 2.i compute the standard deviation of the daily differencies of the forward rates over ,say, 90 days.3. i multilply that numred for sqtr(252) i.e. i "annualize" them4. i try to compare that number to compare with the volatility surface (yield vols) quoted by a broket. Well, what i get is a pretty flat surface, as opposed to a nicely "sliding" surface of the yield vols.......i.e. i get the same volatility on the 1y1y and the 20y20.. while the implied yield vol on the first is about twice the latter....Nothing change if i try to compare the normalised vols....So what i'm missing? Should i consider the tenor of the life of the option to compute the historical volatility? ie. one years of data to get the 1y1y and 20y of data (!!!) to compute the vol of the 20y20y??Thanks,a glabrous cactus

QuoteOriginally posted by: CactusHi,I'm trying to construct something giving me a ratio between realized and implied volatility on the swaption market.So : 1. i compute the forward rates 2.i compute the standard deviation of the daily differencies of the forward rates over ,say, 90 days.3. i multilply that numred for sqtr(252) i.e. i "annualize" them4. i try to compare that number to compare with the volatility surface (yield vols) quoted by a broket. Well, what i get is a pretty flat surface, as opposed to a nicely "sliding" surface of the yield vols.......i.e. i get the same volatility on the 1y1y and the 20y20.. while the implied yield vol on the first is about twice the latter....Nothing change if i try to compare the normalised vols....So what i'm missing? Should i consider the tenor of the life of the option to compute the historical volatility? ie. one years of data to get the 1y1y and 20y of data (!!!) to compute the vol of the 20y20y??Thanks,a glabrous cactusYou should use swap rates that would correspond to the "yield" vols quoted by the broker. As for not matching the quoted vol surface - i am willing to bet that you will see no correlation between implied and historical vols. Swaption vols are allways humped, since we expect the most vol in short term with mean reversion later on. It does not work this way in real life.

I don't understand, what you mean with"..You should use swap rates that would correspond to the "yield" vols....". The rates i use to compute is the exact ATM fwrd rate for eache swaption..... However i was surprised discovering that the yield vol (or also normalised vols) surface is not reflected in the historical perspective: I supposed the 1y1y fwrd rated being historically more volatile than the 10y10y rate....CACTUS

Hi,are you sure you should be using fwd rates to compute historical volatilities?Isn't the implied vol a reflection of the anticipated vol of the underlying fwd rate as it rolls down into spot?In other words, I think the underlying used to calculate historical vol should be e.g. the 1y1y rate today, the 6m1y rate in 6mths, ... the spot rate in 1y. As a consequence, wouldn't it be more accurate to use some weighted average between historical vols of spot and fwd rates? The difference should be minor if you do the exercise for, say 6m10y swaptions, but it should be significant if you are looking at lower tenors like 1y1y where the fwd is much more volatile than the spot. Or am I missing something? Anybody any comments?

You should intergrate the volatility of forward rate to get the volatility of the swap rate.

Cactus, in your step. 2 when you wrote that you compute the standard deviation of the daily differencies of the forward rates, do you compute absolute differences or log differences? (eg. R2-R1 or Log(R2/R1))? To be consistent with Black and therefore with quoted implied Black vols, it should the log ones.In addition, I don't think that computing standard deviation over 90 days is that great to estimate vol. A bit better could be to use the EWMA method (the one use within the riskmetrics VaR framework).JM

i would say the log returns should be used.i have been using historical swaption vols and these depend a great deal on which market ( how liquid) is being considered.one should calculate forward swap rates(yields) and take standard deviations over a sufficiently long period (30 to 100 days atleast).